CN117685123A - High-pressure common rail fuel system fuel injection rule prediction method based on rail pressure fluctuation model - Google Patents

Abstract

The invention discloses a rail pressure fluctuation model-based high-pressure common rail fuel system fuel injection rule prediction method, which belongs to the technical field of diesel engine fuel systems and comprises the following steps: 1) Establishing a rail pressure fluctuation model; 2) Establishing a discretized state space model according to the rail pressure fluctuation model in the step 1); 3) Rail pressure fluctuation optimal estimation based on Kalman filter; 4) And calculating an oil injection rule by using the optimal rail pressure drop estimation result. The rail pressure observer based on Kalman filtering is designed on the basis, and the rail pressure dropping process obtained by observation is utilized to realize real-time observation and calculation of the oil injection rate and the oil injection quantity of the high-pressure common rail system.

Description

A prediction of injection regularity of high-pressure common rail fuel system based on rail pressure fluctuation model method

Technical field

The invention belongs to the technical field of diesel engine fuel systems, and specifically relates to a real-time prediction method of fuel injection rules suitable for high-pressure common rail fuel systems.

Background technique

At present, the fuel injection quantity control of the diesel engine high-pressure common rail system is based on the open-loop control mode of the calibrated MAP chart, and the fuel injection information cannot be measured in real time during actual operation. Due to factors such as changes in system operating conditions and degradation of structural parameters, Influence, it is often difficult to ensure the consistency and reliability of cycle injection performance. If the injection information can be monitored in real time during the actual operation of the diesel engine, so as to make closed-loop adjustments and corrections to the injection pattern, the accuracy of injection control can be greatly improved.

The instantaneous drop in pressure caused by the fuel injection process directly reflects the information of the fuel injection process. Currently, the research on fuel injection prediction based on the fuel pressure signal mainly involves establishing a dynamic mathematical model and numerically solving it to calculate the fuel injection amount. These methods are essentially open-ended. Ring calculation, due to factors such as modeling errors, improper initial condition settings, noise interference, etc., there are large errors in the calculated fuel injection volume results. In response to this limitation, the inventor has applied for a Chinese patent for "A method for predicting the fuel injection volume of a high-pressure common rail system based on a closed-loop observer", which introduces the idea of closed-loop feedback correction and realizes real-time observation and closed-loop correction of the cyclic fuel injection volume. (Chinese patent: ZL202010577723.3, this patent has been authorized). On this basis, when the rail pressure changes in a large range, the model parameters change with the operating conditions, and the system has large nonlinearity. The inventor uses the Kalman filter algorithm to optimize the observation process, which can estimate the state variables and provide feedback. The gain undergoes continuous iteration and rolling optimization (Chinese patent: CN2022112886412). However, the above method only considers the impact of the fuel injection process on pressure fluctuations, that is, it only models the situation when the fuel injection process does not supply fuel. This method is suitable for situations where the fuel injection process and the fuel supply process do not overlap. When the fuel supply process overlaps with the fuel injection process, the rail pressure drop process caused by fuel injection will be affected by the fuel supply process, and the fuel injection observation model established above is no longer applicable.

Contents of the invention

In order to solve the above problems, the present invention proposes a method for predicting the injection pattern of a high-pressure common rail fuel system based on an optimized rail pressure fluctuation model, taking into account the rail pressure drop process caused by fuel injection, and the rail pressure caused by fuel supply. During the rising process, a rail pressure fluctuation model was established. This model also considers the impact of the fuel injection and fuel supply processes on pressure fluctuations, and can reflect the pressure fluctuation pattern more comprehensively and accurately. On this basis, a rail pressure fluctuation model based on Kalman filtering is designed. The observer uses the observed rail pressure drop process to realize real-time observation and calculation of the fuel injection rate and fuel injection volume of the high-pressure common rail system. Note: In the present invention, (·) is the first-order derivative, (··) is the second-order derivative, and (^) is the estimated value.

The technical solutions adopted by the present invention are as follows:

A method for predicting the injection pattern of a high-pressure common rail fuel system based on an optimized rail pressure fluctuation model. The method includes the following steps:

1) Establish a rail pressure fluctuation model;

2) Establish a discretized state space model based on the rail pressure fluctuation model in step 1);

3) Optimal estimation of rail pressure fluctuation based on Kalman filter;

4) Use the optimal estimation results of rail pressure drop to calculate the fuel injection pattern;

Among them, step 1) establishes the rail pressure fluctuation model as:

The rail pressure change p is the instantaneous rail pressure fluctuation after subtracting the steady-state value p _ss , which is composed of the superposition of the rising process and the falling process, and is expressed as:

p(t)＝p _down (t)+p _up (t) (1)

Among them, the rail pressure drop stage model:

Proportional coefficient K _down (p _ss ) = K (p _ss )·α (p _ss ), its value is equal to the ratio of the rail pressure drop during the injection process to the corresponding injection pulse width; K is the proportional coefficient, its value depends on Target rail pressure; τ _down is the time constant of the injection rate output response;

C _loss is the fuel loss coefficient, and its value is the ratio of Q _inj to Q _loss . The steady-state value p _ss is the target rail pressure under the current working condition, V ₀ is the initial volume of the common rail pipe, and ΔV (p _ss ) is the volume of the common rail pipe. Compensation amount, injection timing signal u _inj (t) is a pulse width modulation signal

The period T is the injection interval, the injection start time t _start is determined by the moment when the rail pressure begins to decrease, and the end time t _end is determined by the injection duration;

Rail pressure rising stage model:

p _up (t) is the rail pressure rise, τ _up is the inertia time constant of the output response during the rail pressure rise process, and the proportional coefficient K _up (p _ss ) is the ratio of the rail pressure rise to the corresponding fuel supply;

u _pump (t) is the step input of the fuel supply amount. The amplitude of the step input signal is the reference fuel supply amount of the current working condition. The step input action time t _step can be determined by the moment when the rail pressure starts to rise;

The discretized state space model in step 2) is:

In the formula, k represents the number of sampling points, C _d =C = [1 0 1]; the output y is the instantaneous rail pressure fluctuation p after subtracting the steady-state value; the input signal u = [u _inj u _pump ] ^T ; Including rail pressure drop amount p _down and rail pressure drop rate/> The three variables of rail pressure rise p _up are used as state variables;

Step 3) The steps for optimal estimation of rail pressure fluctuations based on Kalman filter are:

Considering the model uncertainty w _u (k) and the measurement noise v (k), the discrete system state space model is expressed as:

Among them, the input process noise w _u (k) is [w _inj (k)w _pump (k)] ^T ; w _u (k) and v (k) are assumed to be mutually uncorrelated zero-mean Gaussian white noise, and their covariance The matrices are Q and R respectively;

Since B _d in model (19) changes with changes in rail pressure operating conditions, in order to adapt to changes in operating conditions, the process noise covariance matrix Q can be optimally designed as a time-varying matrix:

Q(k)＝B _d (k)E[w _u (k)w _u (k) ^T ]B _d (k) ^T (6)

Setting the initial value and P(0) ⁺ , and after setting Q and R,

① Calculate a priori estimate

②Calculate the covariance matrix P(k) of the a priori estimation error ^- :

P(k) ^- =Α _d (k-1)P(k-1) ⁺ A _d (k-1) ^T +Q(k-1) (8)

③Calculate the Kalman feedback gain K(k) ^based on P(k):

K(k)＝P(k) ^- C _d (k) ^T [C _d (k)P(k) ^- C _d (k) ^T +R(k)] ^-1 (9)

④At the kth moment, output the measured value y(k) and the prior estimate The difference is used as feedback to correct the prior estimate and obtain the posterior estimate/>

⑤Calculate the posterior covariance matrix P(k) ⁺ :

P(k) ⁺ =(IK(k)C _d (k))P(k) ^- (IK(k)C _d (k)) ^T +K(k)R(k)K(k) ^T (11 )

Through the cycle of steps ① to ⑤, the system state, error covariance matrix and Kalman filter gain are continuously updated to make the posterior estimate value approach the true value, that is, the posterior error approaches 0, and the state variables of the high-voltage common rail system are completed. the best estimate;

Step 4) The steps to calculate the fuel injection pattern using the optimal estimation results of rail pressure drop are:

Use the estimated value of the state variables of the medium and high-voltage common rail system in step 3) Calculate the fuel injection rate according to equation (4):

In the formula, C _loss is the fuel loss coefficient; under a certain rail pressure p ₁ , this coefficient is related to the fuel leakage volume V _leak , the oil return volume V _re and the fuel injection volume V _inj :

Use experiments or simulation methods to measure the data of V _leak , V _re and V _inj under the set rail pressure p ₁ , and obtain C _loss (p ₁ ) according to Equation (14), and change the rail pressure to obtain different set rail pressures. C _loss under , apply least squares to fit C _loss (p _ss ) when the derailment pressure range is large;

Will Perform summation within the fuel injection stage to obtain the fuel injection quantity observation value/>

The advantages of the present invention are:

1. According to the influence of the fuel injection process and the fuel supply process on the rail pressure change, the transfer functions between the fuel injection and the rail pressure drop section, and the fuel supply and the rail pressure rise section were established, and the rail pressure drop amount p _down , rail pressure Pressure drop rate The three variables of rail pressure rise amount p _up are used to construct a considerable state space model. This model can be applied to the observation of rail pressure fluctuations when fuel supply and fuel injection overlap.

2. Taking the model uncertainty and the influence of measurement noise into consideration in the model, an optimal estimation method of the injection pattern based on the Kalman filter algorithm is proposed. The feedback gain matrix is updated in real time by using the recursion principle of Kalman filter, and the process noise covariance matrix Q is optimized and designed to adapt to the changes in rail pressure operating conditions in a wide range. This obtains the optimal estimation result of the rail pressure drop process caused by fuel injection, thereby achieving online real-time and accurate observation of fuel injection information.

Description of the drawings

In order to explain the technical solutions of the present invention more clearly, the drawings needed to be used in the description of the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present invention, and are not useful in this field. For those skilled in the art, all other embodiments obtained without any creative effort fall within the scope of protection of the present invention.

Figure 1 Schematic diagram of the injection pattern observation method based on rail pressure fluctuations

Figure 2 Schematic diagram of the rail pressure fluctuation Kalman filter process

Figure 3 Injection timing input signal

Figure 4 Fuel supply step input signal

Figure 5 Actual rail pressure and observed pressure when injection and fuel supply do not overlap

Figure 6. The measured fuel injection rate and the observed fuel injection rate when the fuel injection and fuel supply do not overlap.

Figure 7 The measured fuel injection volume and the observed fuel injection volume when the fuel injection and fuel supply do not overlap

Figure 8 Actual rail pressure and observed pressure when injection and fuel supply overlap

Figure 9 The measured fuel injection rate and the observed fuel injection rate when the injection and fuel supply overlap

Figure 10 Measured fuel injection volume and observed fuel injection volume when injection and fuel supply overlap

Detailed ways

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other implementations obtained by those skilled in the art without creative efforts fall within the scope of protection of the present invention.

Figure 1 is a schematic diagram of an embodiment of the present invention providing a method for observing the injection pattern of a high-pressure common rail system based on optimal estimation of rail pressure fluctuations. The rail pressure signal is measured in real time through the pressure sensor on the common rail pipe; the signal is input into the designed rail pressure Kalman filter to obtain the optimal estimation result of the rail pressure drop stage caused by fuel injection; the rail pressure drop estimation is used The fuel injection rate is calculated as a result; the fuel injection rate is integrated and calculated during the fuel injection stage to obtain the predicted fuel injection volume.

Figure 2 is a schematic diagram of the design process of the Kalman filter for rail pressure fluctuations. First, based on the impact of the fuel injection process and the fuel supply process on rail pressure fluctuations, the dynamic models between the fuel injection and rail pressure drop sections, and the fuel supply and rail pressure rise sections were respectively established. State variables were selected to construct a rail pressure fluctuation state space model. And carry out discretization; based on this, considering the influence of model uncertainty and measurement noise, a rail pressure fluctuation Kalman filter is designed, using the recursion principle, the difference between the rail pressure signal measured in real time by the rail pressure sensor and the estimated value is used as feedback Make corrections and continuously update the system state and covariance matrix to achieve the optimal estimate of the rail pressure reduction process.

Each is explained in detail below.

Step 1: Establish rail pressure fluctuation model

Assuming that the fuel pressure in the common rail pipe is uniformly distributed, the fuel continuity equation of the common rail pipe is expressed as:

In the formula, p is the instantaneous rail pressure fluctuation after subtracting the steady-state value p _ss , and the steady-state value p _ss is the target rail pressure under the current operating condition; Q _pump is the fuel supply rate; Q _inj is the fuel injection rate; Q _loss is the fuel Loss rate; E is the fuel volume elastic modulus; V is the common rail tube control volume.

Ignoring changes in fuel temperature during operation, E is related to rail pressure conditions, and the empirical formula is:

E＝1.2×10 ⁴ (1+0.001p _ss ) (2)

The common rail pipe is affected by high-pressure fuel, and V changes with the rail pressure working conditions. Suppose V consists of the initial volume V ₀ of the common rail pipe and its compensation amount ΔV, that is:

V＝V ₀ +△V(p _ss ) (3)

During fuel injection, the fuel injection causes the pressure in the common rail pipe to drop instantaneously; during fuel supply, the high-pressure oil pump supplies high-pressure fuel to the common rail pipe, causing the rail pressure to rise instantaneously. In order to decouple the influence of the fuel injection process and the fuel supply process on the rail pressure fluctuation, the rail pressure p can be decomposed into the rail pressure drop process p _down and the rail pressure rise process p _up , and the fuel injection process, rail pressure drop, and fuel supply processes are established respectively. relationship with the rise in rail pressure.

Step 1.1: Establish a model between the fuel injection process and the rail pressure drop section

The mathematical model between the fuel injection rate Q _inj and the rail pressure drop p _down can be simplified from equation (1):

In the formula, C _loss is the fuel loss coefficient, and its value is the ratio of Q _inj to Q _loss . According to equations (2) to (4), the value of α( _pss ) is related to the target rail pressure working condition, and can be approximately regarded as a constant under a certain rail pressure working condition.

Obviously, there is an integral relationship between the fuel injection rate and the rail pressure drop. Since the fuel injection rate signal cannot be obtained in real time during actual operation, and the fuel injection rate can be determined by the fuel injection timing and the fuel injection pulse width, the present invention uses the fuel injection timing signal u _inj (t) as input to establish a rail pressure drop stage model.

The injection timing signal u _inj (t) is a pulse width modulation signal, its period T is the injection interval, and the duty cycle is the ratio of the injection duration to the injection interval. The fuel injection start time t _start is determined by the moment when the rail pressure begins to decrease, and the end time t _end is determined by the fuel injection duration. The signal is shown in Figure 3, and its expression can be described as

Considering that there is a certain inertia between the injection timing signal u _inj (t) and the injection rate Q _inj (t), the dynamic model between the two can be expressed as:

In the formula, K is the proportional coefficient, and its value depends on the target rail pressure; τ _down is the time constant of the injection rate output response. Since the response at the beginning and end of the injection rate response is extremely fast, the inertia time constants under different working conditions are similar, and τ _down can be regarded as a constant.

Substitute Equation (5) into Equation (6) to obtain the rail pressure drop stage model with u _inj (t) as input and p _down (t) as output:

In the formula, the proportional coefficient K _down (p _ss ) = K (p _ss )·α (p _ss ), and its value is equal to the ratio of the rail pressure drop during the injection process to the corresponding injection pulse width.

Step 1.2: Establish a model between the fuel supply process and the rail pressure rising section

From formula (1), the mathematical model between the fuel supply rate Q _pump and the rail pressure rise p _up can be obtained:

However, the fuel supply rate cannot be measured in real time, and since the duration of the fuel supply phase is unclear, a time series signal cannot be constructed. The reference fuel supply volume V _pump of the current working condition can only be obtained by searching the pre-calibrated fuel supply volume MAP map under each working condition (different speeds, rail pressures, and fuel metering valve openings). The difference between the fuel supply volume and the fuel supply rate It is a point relationship. Therefore, the present invention constructs a fuel supply amount step signal u _pump (t) as the input of the rail pressure rising stage. The amplitude of the step input signal is the reference fuel supply amount under the current working condition. The step input action time t _step can be determined according to the rail pressure rising time, as shown in Figure 4.

Considering that there is a certain inertia in the pressure rise process, the dynamic model between the rail pressure rise p _up and the fuel supply step input u _pump (t) is expressed as:

In the formula, the proportional coefficient K _up is the ratio of the rail pressure rise to the corresponding fuel supply; τ _up is the inertia time constant of the output response during the rail pressure rise process, and its value can be regarded as a constant under different working conditions.

Although the fuel injection process and the fuel supply process are modeled separately, these models are equally applicable when they occur simultaneously. The rail pressure change p is the superposition of the rising process and the falling process, and is expressed as:

p(t)＝p _down (t)+p _up (t) (10)

Step 1.3: Identify model coefficients

The model of the rail pressure drop stage contains two undetermined coefficients: K _down and τ _down . Among them, K _down is the ratio of the rail pressure drop corresponding to one injection of fuel under the current working condition and the corresponding injection pulse width, which is related to the rail pressure working condition. The present invention is aimed at a high-pressure common rail system with four injectors, double plungers and double-acting cam driven high-pressure oil pumps. Taking the rail pressure of 1200bar and the camshaft speed of 1000r/min as an example, the rail pressure drop with different pulse widths is obtained. The calculated K _down is shown in Table 1.

Table 1 Rail pressure drop parameters and K _down

K _down is similar under different injection pulse widths, so the average value of K _down under the current rail pressure condition is -44768. When the set rail pressure changes, repeat this step to obtain the model coefficients under a wide range of rail pressure changes to adapt to calculations under different working conditions. The K _down expression fitted by this system under different working conditions is:

K _down (p _ss )＝-7769-29.51·p _ss (11)

According to the first-order system characteristics, the time constant τ _down is the time for the injection rate to reach 0.632 times the steady-state value from 0. The fuel injection rate curve rises and falls very quickly under different working conditions, and τ _down takes a constant value of 0.00015.

The model during the rail pressure rising stage also contains two undetermined coefficients: K _up and τ _up . According to equation (8), the expression of K _up can be written as:

In the formula, according to the common rail tube structural parameters, V ₀ =29061mm ³ , the compensation amount ΔV(p _ss ) =5.048·p _ss .

In the case of step input, the time constant τ _up is the time for the rail pressure rise output response to reach 0.632 times the steady-state amplitude from 0. The average value of τ _up under different working conditions is taken, which is 0.0019.

Step 2: Construct the rail pressure state space model and discretize it

Based on the transfer function model established above, a state space model of rail pressure fluctuation is established. Three variables are selected as the state variables: rail pressure drop p _down , rail pressure drop rate p _down , and rail pressure rise p _up , namely

According to equation (7), equation (9) and equation (10), the state space model is obtained as follows:

In the formula, C=[1 0 1]. The output y is the instantaneous rail pressure change p after subtracting the steady-state value; the input signal u=[u _inj u _pump ] ^T .

Determine the observability of the system. The observable matrix Lo of model (13) is calculated as follows:

Lo is full rank, indicating that the system is considerable and can be designed as a rail voltage drop Kalman filter.

Before designing the Kalman filter observer, the state space model of the continuous system needs to be discretized. When the sampling step size is Δt, the derivative of the state variable x(t) at time t _k can be approximately expressed as:

The above formula can be transformed into:

In the formula,

The sampling time t _k in equation (16) is uniformly represented by the number of sampling points k, that is:

x(k)＝A _d x(k-1)+B _d u(k-1) (17)

Then the discrete state space model can be expressed as:

In the formula, C _d =C = [101].

Step 3: Optimal estimation of rail voltage drop based on Kalman filter

Considering the model uncertainty w _u (k) and the measurement noise v (k), the system state space model is expressed as:

Among them, the input process noise w _u (k) is [w _inj (k)w _pump (k)] ^T . w _u (k) and v (k) are assumed to be mutually uncorrelated zero-mean Gaussian white noise, and their covariance matrices are Q and R respectively.

According to the Kalman filter algorithm, the estimated value of the state variable at the kth moment is defined as It is also divided into a priori estimate/> Posterior estimate/> The algorithm includes two stages: time update and measurement update: the time update stage uses the system model to calculate the state prior estimate, and the measurement update stage uses the error between the rail pressure measurement value and the prior estimate to perform feedback correction and calculate the posterior estimate. value.

Kalman filter performance is determined by the noise covariance matrices Q and R. The measurement noise covariance matrix R depends on the degree of filtering of the measurement signal. Since B _d in model (19) changes with changes in rail pressure operating conditions, in order to adapt to changes in operating conditions, the process noise covariance matrix Q can be optimally designed as a time-varying matrix:

Q(k)＝B _d (k)E[w _u (k)w _u (k) ^T ]B _d (k) ^T (20)

Setting the initial value and P(0) ⁺ , and after selecting appropriate Q and R, you can loop according to equations (21) to (25) to continuously update the system state, error covariance matrix and Kalman filter gain to make the posterior estimate The value approaches the true value, that is, the posterior error approaches 0, and the optimal estimation of the state variables of the high-voltage common rail system can be completed.

Time update stage:

①Use model (18) to calculate the prior estimate

②Calculate the covariance matrix P(k) of the a priori estimation error ^- :

P(k) ^- ＝Α _d (k-1)P(k-1) ⁺ Α _d (k-1) ^T +Q(k-1) (22)

③Calculate the Kalman feedback gain K(k) ^based on P(k):

K(k)＝P(k) ^- C _d (k) ^T [C _d (k)P(k) ^- C _d (k) ^T +R(k)] ^-1 (23)

④At the kth moment, output the measured value y(k) and the prior estimate The difference is used as feedback to correct the prior estimate and obtain the posterior estimate/>

⑤Calculate the posterior covariance matrix P(k) ⁺ :

P(k) ⁺ =(IK(k)C _d (k))P(k) ^- (IK(k)C _d (k)) ^T +K(k)R(k)K(k) ^T (25 )

At time k, the posterior estimate is obtained according to equation (24) in/> with/> That is, the optimal estimation result of rail pressure drop amount and rail pressure drop rate, output/> That is the rail pressure filtering result/>

Step 4: Use the optimal estimation result of rail pressure drop to calculate the fuel injection pattern

get After that, the fuel injection rate can be calculated according to equation (4):

In the formula, C _loss is the fuel loss coefficient. Under a certain set rail pressure p ₁ , this coefficient is related to the fuel leakage amount V _leak , the oil return amount V _re and the fuel injection amount V _inj :

Use experiments or simulation methods to measure the data of V _leak , V _re and V _inj under the set rail pressure p ₁ , and obtain C _loss (p ₁ ) according to Equation (27), and change the rail pressure to obtain different set rail pressures. C _loss under , apply the least squares method to fit C _loss (p _ss ) when the derailment pressure range is large. The C _loss (p _ss ) obtained by fitting in this example is:

C _loss (p _ss )＝0.2115+5.85×10 ^-6 ·p _ss (28)

Will Perform summation within the fuel injection stage to obtain the fuel injection quantity observation value/>

In order to verify the filtering effect and observation accuracy of the observation method under different working conditions, a simulation study was conducted using the method proposed by the present invention under the working conditions of 1200 bar rail pressure and 1.2 ms fuel injection pulse width. Figures 5 to 7 show the observation results of common rail pressure, fuel injection rate, and fuel injection volume when the injection and fuel supply do not overlap. Figures 8 to 10 show the observation results of rail pressure, fuel injection rate, and fuel injection volume when the ratio of the number of fuel injections to the number of fuel supplies per cycle is 6:4. It can be seen that rapid tracking of rail pressure and fuel injection rate can be achieved under both working conditions. Comparing the actual values of the single injection injection quantity observation results, the errors are shown in Table 2 below:

Table 2 Observation error of fuel injection quantity under different working conditions

Working conditions maximum error minimum error average error Injection fuel supply does not overlap 4.62% 1.06% 2.62% There is overlap in fuel injection and fuel supply 4.86% 0.20% 2.55%

.

Claims (1)

1. A method for predicting an oil injection rule of a high-pressure common rail fuel system based on a rail pressure fluctuation model is characterized by comprising the following steps:

1) Establishing a rail pressure fluctuation model;

2) Establishing a discretized state space model according to the rail pressure fluctuation model in the step 1);

3) Rail pressure fluctuation optimal estimation based on Kalman filter;

4) Calculating an oil injection rule by using an optimal rail pressure drop estimation result;

wherein, step 1) establishes the rail pressure fluctuation model as:

the rail pressure change p being the subtraction of the steady state value p _ss The instantaneous rail pressure fluctuation after is formed by superposition of an ascending process and a descending process, and is expressed as follows:

p(t)＝p _down (t)+p _up (t) (1)

wherein, the rail pressure decline stage model:

scaling factor K _down (p _ss )＝K(p _ss )·α(p _ss ) The value of the fuel injection valve is equal to the ratio of the rail pressure drop amount in the fuel injection process to the corresponding fuel injection pulse width; k is a proportionality coefficient, the value of which depends on the target rail pressure; τ _down Outputting a response time constant for the fuel injection rate;

C _loss for fuel loss coefficientHaving a value of Q _inj And Q is equal to _loss Ratio of steady state value p _ss For the current working condition target rail pressure, V ₀ For the initial volume of the common rail, deltaV (p _ss ) For the volume compensation of the common rail pipe, the oil injection time sequence signal u _inj (t) is a pulse width modulated signal

The period T is the oil injection interval, and the oil injection starting time T _start Determined by the beginning descending moment of rail pressure and ending moment t _end Determined by the duration of the injection;

track pressure rising stage model:

p _up (t) is the rail pressure rise, τ _up Inertial time constant of output response for rail pressure rise process, proportionality coefficient K _up (p _ss ) Is the ratio of the rail pressure rise to the corresponding oil supply;

u _pump (t) is the step input of the oil supply quantity, the amplitude of the step input signal is the reference oil supply quantity of the current working condition, and the action time t of the step input _step Can be determined by the moment when the rail pressure starts to rise;

the discretized state space model in step 2) is:

where k represents the number of sampling points,C _d ＝C＝[1 0 1]the method comprises the steps of carrying out a first treatment on the surface of the The output y is the instantaneous rail pressure fluctuation p after subtracting the steady state value; input signal u= [ u ] _inj u _pump ] ^T ；Comprising the rail pressure drop p _down Rail pressure drop Rate->Track pressure rise p _up Three variables are used as state variables;

the step 3) of rail pressure fluctuation optimal estimation based on a Kalman filter comprises the following steps:

consider model uncertainty w _u (k) And measuring noise v (k), the discrete system state space model being expressed as:

wherein the process noise w is input _u (k) Is [ w ] _inj (k)w _pump (k)] ^T ；w _u (k) Zero-mean Gaussian white noise which is assumed to be uncorrelated with v (k) has covariance matrices of Q and R respectively;

due to B in the model (19) _d The process noise covariance matrix Q can be optimally designed into a time-varying matrix to adapt to the working condition change along with the change of the rail pressure working condition:

Q(k)＝B _d (k)E[w _u (k)w _u (k) ^T ]B _d (k) ^T (6)

at a set initial valueAnd P (0) ⁺ After Q and R are set, the method comprises the steps of,

(1) calculating a priori estimates

(2) Calculating covariance matrix P (k) of prior estimation error ^- ：

P(k) ^- ＝Α _d (k-1)P(k-1) ⁺ Α _d (k-1) ^T +Q(k-1) (8)

(3) According to P (k) ^- Calculating a Kalman feedback gain K (K):

K(k)＝P(k) ^- C _d (k) ^T [C _d (k)P(k) ^- C _d (k) ^T +R(k)] ^-1 (9)

(4) at the kth time, output by measurement y (k) and a priori estimateThe difference is used as feedback to correct the prior estimated value to obtain the posterior estimated value +.>

(5) Calculating a posterior covariance matrix P (k) ⁺ ：

P(k) ⁺ ＝(I-K(k)C _d (k))P(k) ^- (I-K(k)C _d (k)) ^T +K(k)R(k)K(k) ^T (11)

Continuously updating the system state, the error covariance matrix and the Kalman filtering gain through the circulation of the steps (1) to (5), enabling the posterior estimation value to approach to a true value, namely enabling the posterior error to approach to 0, and completing the optimal estimation of the state variable of the high-voltage common rail system;

the step 4) of calculating the fuel injection rule by utilizing the optimal rail pressure drop estimation result comprises the following steps:

using the state variable estimated value of the high-pressure common rail system in the step 3)Calculating the fuel injection rate according to formula (4):

wherein C is _loss Is the fuel loss coefficient; at a certain rail pressure p ₁ Under the condition, the coefficient and the fuel leakage quantity V _leak Oil return amount V _re And fuel injection quantity V _inj The following are related:

by experimental or simulation means, the set rail pressure p is measured ₁ V below _leak 、V _re And V _inj According to formula (14) to obtain C _loss (p ₁ ) And changing the rail pressure to obtain C under different set rail pressures _loss C when the rail pressure is large in range by least square fitting _loss (p _ss )；

Will beSumming in the oil injection stage to obtain oil injection quantity observation value +.>